Abstract
The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.
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